Oracle Scratchpad

July 17, 2015

Descending Indexes

Filed under: CBO,Oracle,Statistics,Troubleshooting — Jonathan Lewis @ 8:42 am GMT Jul 17,2015

I’ve written about optimizer defects with descending indexes before now but a problem came up on the OTN database forum a few days ago that made me decide to look very closely at an example where the arithmetic was clearly defective. The problem revolves around a table with two indexes, one on a date column (TH_UPDATE_TIMESTAMP) and the other a compound index which starts with the same column in descending order (TH_UPDATE_TIMESTAMP DESC, TH_TXN_CODE). The optimizer was picking the “descending” index in cases where it was clearly the wrong index (even after the statistics had been refreshed and all the usual errors relating to date-based indexes had been discounted). Here’s an execution plan from the system which shows that there’s something wrong with the optimizer:


| Id  | Operation          | Name             | Rows  | Bytes | Cost (%CPU)| Time     |
|   0 | SELECT STATEMENT   |                  |       |       |     4 (100)|          |
|   1 |  SORT AGGREGATE    |                  |     1 |     8 |            |          |
|*  2 |   FILTER           |                  |       |       |            |          |
|*  3 |    INDEX RANGE SCAN| TXN_HEADER_IDX17 |  1083K|  8462K|     4   (0)| 00:00:01 |

There are two clues here: first, Oracle has used the (larger) two-column index when the single column is (almost guaranteed to be) the better choice simply because it will be smaller; secondly, we have a cost of 4 to acquire 1M rowids through an (implicitly b-tree) index range scan, which would require at least 250,000 index entries per leaf block to keep the cost that low (or 2,500 if you set the optimizer_index_cost_adj to 1; so it might just be possible if you had a 32KB block size).

The OP worked hard to supply information we asked for, and to follow up any suggestions we made; in the course of this we got the information that the table had about 90M rows and this “timestamp” column had about 45M distinct values ranging from 6th Sept 2012 to 2nd July 2015 with no nulls.

Based on this information I modelled the problem in an instance of (the OP was using

rem     Script:         descending_bug_05.sql
rem     Author:         Jonathan Lewis
rem     Dated:          Apr 2015

create table t1
with generator as (
        select  --+ materialize
                rownum id
        from dual
        connect by
                level <= 1e4  -- > comment to avoid wordpress format issue
        rownum                                                          id,
        to_date('06-SEP-2012 15:13:00','dd-mon-yyyy hh24:mi:ss') +
                trunc((rownum - 1 )/4) / (24 * 60)                      upd_timestamp,
        mod(rownum - 1,10)                                              txn_code,
        rpad('x',50)                                                    padding
        generator       v1,
        generator       v2
        rownum <= 4 * 1030  *  24 * 60  -- > comment to avoid wordpress format issue

create index t1_asc on t1(upd_timestamp) nologging;
create index t1_desc on t1(upd_timestamp desc) nologging;

                ownname          => user,
                tabname          => 'T1',
                method_opt       => 'for all columns size 1',
                cascade          => false

My data set has 4 rows per minute from 6th Sept 2012 to 3rd July 2015, with both an ascending and descending index on the upd_timestamp column. For reference, here are the statistics about the two indexes:

-------------------- ---------- ---------- ----------- -----------------
T1_DESC                 5932800          2       17379            154559
T1_ASC                  5932800          2       15737             59825

The ascending index is smaller with a significantly better clustering_factor, so for queries where either index would be a viable option the ascending index is the one (we think) that the optimizer should choose. In passing, the 5.9M index entries is exactly the number of rows in the table – these stats were computed automatically as the indexes were created.

Here’s a simple query with execution plan (with rowsource execution stats) pulled from memory and edited to avoid a WordPress formatting issue:

select max(id) from t1 where upd_timestamp between
to_date('01-jun-2015','dd-mon-yyyy')                and

| Id  | Operation                    | Name    | Starts | E-Rows | Cost (%CPU)| A-Rows |   A-Time   | Buffers |
|   0 | SELECT STATEMENT             |         |      1 |        |    29 (100)|      1 |00:00:01.29 |    4710 |
|   1 |  SORT AGGREGATE              |         |      1 |      1 |            |      1 |00:00:01.29 |    4710 |
|   2 |   TABLE ACCESS BY INDEX ROWID| T1      |      1 |    167K|    29   (0)|    167K|00:00:00.98 |    4710 |
|*  3 |    INDEX RANGE SCAN          | T1_DESC |      1 |    885 |     5   (0)|    167K|00:00:00.35 |     492 |

Predicate Information (identified by operation id):
   3 - access("T1"."SYS_NC00005$" .ge. HEXTORAW('878CF9E1FEF8FEFAFF')  AND
              "T1"."SYS_NC00005$" .le. HEXTORAW('878CF9FEF8FEF8FF') )
       filter((SYS_OP_UNDESCEND("T1"."SYS_NC00005$") .ge. TO_DATE(' 2015-06-01 00:00:00', 'syyyy-mm-dd
              hh24:mi:ss') AND SYS_OP_UNDESCEND("T1"."SYS_NC00005$") .le. TO_DATE(' 2015-06-30 00:00:00',
              'syyyy-mm-dd hh24:mi:ss')))

The optimizer’s index estimate of 885 rowids is a long way off the actual rowcount of 167,000 – even though I have perfect stats describing uniform data and the query is simple enough that the optimizer should be able to get a good estimate. Mind you, the predicate section looks a lot messier than you might expect, and the table estimate is correct (though not consistent with the index estimate, of course).

Here’s the plan I get when I make the descending index invisible:

| Id  | Operation                    | Name   | Starts | E-Rows | Cost (%CPU)| A-Rows |   A-Time   | Buffers |
|   0 | SELECT STATEMENT             |        |      1 |        |  2146 (100)|      1 |00:00:01.25 |    2134 |
|   1 |  SORT AGGREGATE              |        |      1 |      1 |            |      1 |00:00:01.25 |    2134 |
|   2 |   TABLE ACCESS BY INDEX ROWID| T1     |      1 |    167K|  2146   (1)|    167K|00:00:00.94 |    2134 |
|*  3 |    INDEX RANGE SCAN          | T1_ASC |      1 |    167K|   453   (2)|    167K|00:00:00.31 |     446 |

Predicate Information (identified by operation id):
   3 - access("UPD_TIMESTAMP" .ge. TO_DATE(' 2015-06-01 00:00:00', 'syyyy-mm-dd hh24:mi:ss') AND
              "UPD_TIMESTAMP" .le. TO_DATE(' 2015-06-30 00:00:00', 'syyyy-mm-dd hh24:mi:ss'))

With the descending index invisible we can see that the cardinality estimate for the ascending index correct and notice how much higher this makes the cost. It’s not surprising that the optimizer picked the wrong index with such a difference in cost. The question now is why did the optimizer get the index cardinality (i.e. selectivity, hence cost) so badly wrong.

The answer is that the optimizer has made the same mistake that applications make by storing dates as character strings. It’s using the normal range-based calculation for the sys_op_descend() values recorded against the virtual column and has lost all understanding of the fact that these values represent dates. I can demonstrate this most easily by creating one more table, inserting a couple of rows, gathering stats, and showing you what the internal storage of a couple of “descending” dates looks like.

drop table t2;

create table t2 (d1 date);
create index t2_i1 on t2(d1 desc);

insert into t2 values('01-Jun-2015');
insert into t2 values('30-Jun-2015');

select d1, sys_nc00002$ from t2;

                ownname          => user,
                tabname          => 'T2',
                method_opt       => 'for all columns size 1',
                cascade          => false

column endpoint_value format 999,999,999,999,999,999,999,999,999,999,999,999
break on table_name skip 1

        table_name, column_name, endpoint_number, endpoint_value, to_char(endpoint_value,'XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX') end_hex
        table_name in ('T1','T2')
and     column_name like 'SYS%'
order by
        table_name, column_name, endpoint_number

I’ve put the dates 1st June 2015 and 30th June 2015 into the table because those were the values I used in the where clause of my query. Here are the results showing the internal representation of the (descending) index column and the stored low and high values for the virtual columns in both t1 and t2.

D1        SYS_NC00002$
--------- ------------------------
01-JUN-15 878CF9FEF8FEF8FF

TABLE_NAME           COLUMN_NAME          ENDPOINT_NUMBER                                   ENDPOINT_VALUE END_HEX
-------------------- -------------------- --------------- ------------------------------------------------ ---------------------------------
T1                   SYS_NC00005$                       0  703,819,340,111,320,000,000,000,000,000,000,000    878CF8FCEFF30BCEBC8823F7000000
                     SYS_NC00005$                       1  703,880,027,955,346,000,000,000,000,000,000,000    878FF6F9EFF20256F3B404F7400000

T2                   SYS_NC00002$                       0  703,819,411,001,549,000,000,000,000,000,000,000    878CF9E1FEF8F24C1C7CED46200000
                     SYS_NC00002$                       1  703,819,419,969,389,000,000,000,000,000,000,000    878CF9FEF8FEEED28AC5B22A200000

If you check the t2 data (sys_nc00002$) values against the end_hex values in the histogram data you’ll see they match up to the first 6 bytes (12 digits). Oracle has done its standard processing – take the first 6 bytes of the column, covert to decimal, round to the most significant 15 digits (technically round(value, -21)), convert and store the result as hex.

So let’s do some arithmetic. The selectivity of a range scan that is in-bounds is (informally): “range we want” / “total range”. I’ve set up t2 to show us the values we will need to calculate the range we want, and I’ve reported the t1 values to allow us to calculate the total range, we just have to subtract the lower value (endpoint number 0) from the higher value for the two sys_nc0000N$ columns. So (ignoring the 21 zeros everywhere) our selectivity is:

  • (703,819,419,969,389 – 703,819,411,001,549) / ( 703,880,027,955,346 – 703,819,340,111,320) = 0.00014777
  • We have 5.9M rows in the table, so the cardinality estimate should be about: 5,932,800 * 0.00014777 = 876.69

The actual cardinality estimate was 885 – but we haven’t allowed for the exact form of the range-based predicate: we should add 1/num_distinct at both ends because the range is a closed range (greater than or EQUAL to, less than or EQUAL to) – which takes the cardinality estimate up to 884.69 which rounds to the 885 that the optimizer produced.


This note shows that Oracle is (at least for dates) losing information about the underlying data when dealing with the virtual columns associated with descending columns in indexes. As demonstrated that can lead to extremely bad selectivity estimates for predicates based on the original columns, and these selectivity estimates make it possible for Oracle to choose the wrong index and introduce a spuriously low cost into the calculation of the full execution plan.


This note seems to match bug note 11072246 “Wrong Cardinality estimations for columns with DESC indexes”, but that bug is reported as fixed in 12.1, while this test case reproduces in More recent tests show that it has been fixed by


  1. hats off Sir, awesome demonstration.

    Comment by vijaysehgal — July 17, 2015 @ 9:51 am GMT Jul 17,2015 | Reply

  2. is this an issue that is due to the fact there is a function (albeit from the optimizer) on the search column
    SYS_OP_UNDESCEND(“T1″.”SYS_NC00005$”) which is hiding the underlying stats from the optimizer – in a similar manner to timestamp with timezone ( a terrible column to search on)

    Comment by Nick Strange — July 17, 2015 @ 1:24 pm GMT Jul 17,2015 | Reply

    • Nick,

      That’s an observation worth making – and could introduce two possible errors.

      Possible error 1: we have two set of predicate where we used to have one and the optimizer might therefore be double counting the selectivity to get an estimate that’s far too low. Fortunately this class of error was recognised as a bug and addressed some time ago (though it’s always possible that the bug-fix didn’t cover every optimizer path), so I didn’t start my investigation with that idea.

      Possible error 2: if (following the bug-fix for double-counting) the optimizer had followed the wrong predicate pair of the two, the sys_op_undescend() function call would probably have introduced one of the “guess factors” of 1/400, giving a cardinality estimate of about 420 – so I suppose I considered that early on in the investigation, but discounted it very quickly without much careful effort.

      Comment by Jonathan Lewis — July 17, 2015 @ 9:18 pm GMT Jul 17,2015 | Reply

  3. […] written in the past about oddities with descending indexes ( here, here, and here, for example) but I’ve just come across a case where I may have to introduce a […]

    Pingback by Descending Problem | Oracle Scratchpad — January 31, 2019 @ 3:34 pm GMT Jan 31,2019 | Reply

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